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https://en.wikipedia.org/wiki/Summation | In mathematics, summation is the addition of a sequence of any kind of numbers, called addends or summands; the result is their sum or total. Beside numbers, other types of values can be summed as well: functions, vectors, matrices, polynomials and, in general, elements of any type of mathematical objects on which an o... |
https://en.wikipedia.org/wiki/Summation%20by%20parts | In mathematics, summation by parts transforms the summation of products of sequences into other summations, often simplifying the computation or (especially) estimation of certain types of sums. It is also called Abel's lemma or Abel transformation, named after Niels Henrik Abel who introduced it in 1826.
Statement
Su... |
https://en.wikipedia.org/wiki/Generalized%20permutation%20matrix | In mathematics, a generalized permutation matrix (or monomial matrix) is a matrix with the same nonzero pattern as a permutation matrix, i.e. there is exactly one nonzero entry in each row and each column. Unlike a permutation matrix, where the nonzero entry must be 1, in a generalized permutation matrix the nonzero en... |
https://en.wikipedia.org/wiki/Diagonalizable%20matrix | In linear algebra, a square matrix is called diagonalizable or non-defective if it is similar to a diagonal matrix, i.e., if there exists an invertible matrix and a diagonal matrix such that or equivalently (Such are not unique.) For a finite-dimensional vector space a linear map is called diagonalizable if th... |
https://en.wikipedia.org/wiki/Axiom%20of%20infinity | In axiomatic set theory and the branches of mathematics and philosophy that use it, the axiom of infinity is one of the axioms of Zermelo–Fraenkel set theory. It guarantees the existence of at least one infinite set, namely a set containing the natural numbers. It was first published by Ernst Zermelo as part of his se... |
https://en.wikipedia.org/wiki/Operator%20norm | In mathematics, the operator norm measures the "size" of certain linear operators by assigning each a real number called its . Formally, it is a norm defined on the space of bounded linear operators between two given normed vector spaces. Informally, the operator norm of a linear map is the maximum factor by which it... |
https://en.wikipedia.org/wiki/K-theory | In mathematics, K-theory is, roughly speaking, the study of a ring generated by vector bundles over a topological space or scheme. In algebraic topology, it is a cohomology theory known as topological K-theory. In algebra and algebraic geometry, it is referred to as algebraic K-theory. It is also a fundamental tool in ... |
https://en.wikipedia.org/wiki/Abelian%20variety | In mathematics, particularly in algebraic geometry, complex analysis and algebraic number theory, an abelian variety is a projective algebraic variety that is also an algebraic group, i.e., has a group law that can be defined by regular functions. Abelian varieties are at the same time among the most studied objects in... |
https://en.wikipedia.org/wiki/Riemann%E2%80%93Roch%20theorem | The Riemann–Roch theorem is an important theorem in mathematics, specifically in complex analysis and algebraic geometry, for the computation of the dimension of the space of meromorphic functions with prescribed zeros and allowed poles. It relates the complex analysis of a connected compact Riemann surface with the su... |
https://en.wikipedia.org/wiki/Partial%20fraction%20decomposition | In algebra, the partial fraction decomposition or partial fraction expansion of a rational fraction (that is, a fraction such that the numerator and the denominator are both polynomials) is an operation that consists of expressing the fraction as a sum of a polynomial (possibly zero) and one or several fractions with a... |
https://en.wikipedia.org/wiki/Free%20abelian%20group | In mathematics, a free abelian group is an abelian group with a basis. Being an abelian group means that it is a set with an addition operation that is associative, commutative, and invertible. A basis, also called an integral basis, is a subset such that every element of the group can be uniquely expressed as an integ... |
https://en.wikipedia.org/wiki/Uniform%20boundedness%20principle | In mathematics, the uniform boundedness principle or Banach–Steinhaus theorem is one of the fundamental results in functional analysis.
Together with the Hahn–Banach theorem and the open mapping theorem, it is considered one of the cornerstones of the field.
In its basic form, it asserts that for a family of continuo... |
https://en.wikipedia.org/wiki/Reciprocity%20law | In mathematics, a reciprocity law is a generalization of the law of quadratic reciprocity to arbitrary monic irreducible polynomials with integer coefficients. Recall that first reciprocity law, quadratic reciprocity, determines when an irreducible polynomial splits into linear terms when reduced mod . That is, it de... |
https://en.wikipedia.org/wiki/Algebraic%20group | In mathematics, an algebraic group is an algebraic variety endowed with a group structure that is compatible with its structure as an algebraic variety. Thus the study of algebraic groups belongs both to algebraic geometry and group theory.
Many groups of geometric transformations are algebraic groups; for example, or... |
https://en.wikipedia.org/wiki/Adele%20ring | In mathematics, the adele ring of a global field (also adelic ring, ring of adeles or ring of adèles) is a central object of class field theory, a branch of algebraic number theory. It is the restricted product of all the completions of the global field and is an example of a self-dual topological ring.
An adele deriv... |
https://en.wikipedia.org/wiki/Restricted%20product | In mathematics, the restricted product is a construction in the theory of topological groups.
Let be an index set; a finite subset of . If is a locally compact group for each , and is an open compact subgroup for each , then the restricted product
is the subset of the product of the 's consisting of all element... |
https://en.wikipedia.org/wiki/Ringed%20space | In mathematics, a ringed space is a family of (commutative) rings parametrized by open subsets of a topological space together with ring homomorphisms that play roles of restrictions. Precisely, it is a topological space equipped with a sheaf of rings called a structure sheaf. It is an abstraction of the concept of the... |
https://en.wikipedia.org/wiki/Inaccessible%20cardinal | In set theory, an uncountable cardinal is inaccessible if it cannot be obtained from smaller cardinals by the usual operations of cardinal arithmetic. More precisely, a cardinal is strongly inaccessible if it satisfies the following three conditions: it is uncountable, it is not a sum of fewer than cardinals smaller... |
https://en.wikipedia.org/wiki/Mahlo%20cardinal | In mathematics, a Mahlo cardinal is a certain kind of large cardinal number. Mahlo cardinals were first described by . As with all large cardinals, none of these varieties of Mahlo cardinals can be proven to exist by ZFC (assuming ZFC is consistent).
A cardinal number is called strongly Mahlo if is strongly inacc... |
https://en.wikipedia.org/wiki/Zero%20sharp | In the mathematical discipline of set theory, 0# (zero sharp, also 0#) is the set of true formulae about indiscernibles and order-indiscernibles in the Gödel constructible universe. It is often encoded as a subset of the integers (using Gödel numbering), or as a subset of the hereditarily finite sets, or as a real numb... |
https://en.wikipedia.org/wiki/Indescribable%20cardinal | In set theory, a branch of mathematics, a Q-indescribable cardinal is a certain kind of large cardinal number that is hard to axiomatize in some language Q. There are many different types of indescribable cardinals corresponding to different choices of languages Q. They were introduced by .
A cardinal number is calle... |
https://en.wikipedia.org/wiki/Measurable%20cardinal | In mathematics, a measurable cardinal is a certain kind of large cardinal number. In order to define the concept, one introduces a two-valued measure on a cardinal , or more generally on any set. For a cardinal , it can be described as a subdivision of all of its subsets into large and small sets such that itself is l... |
https://en.wikipedia.org/wiki/Strong%20cardinal | In set theory, a strong cardinal is a type of large cardinal. It is a weakening of the notion of a supercompact cardinal.
Formal definition
If λ is any ordinal, κ is λ-strong means that κ is a cardinal number and there exists an elementary embedding j from the universe V into a transitive inner model M with critical... |
https://en.wikipedia.org/wiki/Woodin%20cardinal | In set theory, a Woodin cardinal (named for W. Hugh Woodin) is a cardinal number such that for all functions
there exists a cardinal with
and an elementary embedding
from the Von Neumann universe into a transitive inner model with critical point and
An equivalent definition is this: is Woodin if and only i... |
https://en.wikipedia.org/wiki/Superstrong%20cardinal | In mathematics, a cardinal number κ is called superstrong if and only if there exists an elementary embedding j : V → M from V into a transitive inner model M with critical point κ and ⊆ M.
Similarly, a cardinal κ is n-superstrong if and only if there exists an elementary embedding j : V → M from V into a transitive ... |
https://en.wikipedia.org/wiki/Supercompact%20cardinal | In set theory, a supercompact cardinal is a type of large cardinal independently introduced by Solovay and Reinhardt. They display a variety of reflection properties.
Formal definition
If is any ordinal, is -supercompact means that there exists an elementary embedding from the universe into a transitive inner mo... |
https://en.wikipedia.org/wiki/Huge%20cardinal | In mathematics, a cardinal number is called huge if there exists an elementary embedding from into a transitive inner model with critical point and
Here, is the class of all sequences of length whose elements are in .
Huge cardinals were introduced by .
Variants
In what follows, refers to the -th iterate of... |
https://en.wikipedia.org/wiki/Local%20homeomorphism | In mathematics, more specifically topology, a local homeomorphism is a function between topological spaces that, intuitively, preserves local (though not necessarily global) structure.
If is a local homeomorphism, is said to be an étale space over Local homeomorphisms are used in the study of sheaves. Typical exam... |
https://en.wikipedia.org/wiki/Group%20cohomology | In mathematics (more specifically, in homological algebra), group cohomology is a set of mathematical tools used to study groups using cohomology theory, a technique from algebraic topology. Analogous to group representations, group cohomology looks at the group actions of a group G in an associated G-module M to eluci... |
https://en.wikipedia.org/wiki/Typical%20set | In information theory, the typical set is a set of sequences whose probability is close to two raised to the negative power of the entropy of their source distribution. That this set has total probability close to one is a consequence of the asymptotic equipartition property (AEP) which is a kind of law of large number... |
https://en.wikipedia.org/wiki/Algebraic%20variety | Algebraic varieties are the central objects of study in algebraic geometry, a sub-field of mathematics. Classically, an algebraic variety is defined as the set of solutions of a system of polynomial equations over the real or complex numbers. Modern definitions generalize this concept in several different ways, while a... |
https://en.wikipedia.org/wiki/Product%20rule | In calculus, the product rule (or Leibniz rule or Leibniz product rule) is a formula used to find the derivatives of products of two or more functions. For two functions, it may be stated in Lagrange's notation as or in Leibniz's notation as
The rule may be extended or generalized to products of three or more functi... |
https://en.wikipedia.org/wiki/Multiplication%20sign | The multiplication sign, also known as the times sign or the dimension sign, is the symbol ×, used in mathematics to denote the multiplication operation and its resulting product. While similar to a lowercase X (), the form is properly a four-fold rotationally symmetric saltire.
History
The earliest known use of the ... |
https://en.wikipedia.org/wiki/Levi-Civita%20connection | In Riemannian or pseudo-Riemannian geometry (in particular the Lorentzian geometry of general relativity), the Levi-Civita connection is the unique affine connection on the tangent bundle of a manifold (i.e. affine connection) that preserves the (pseudo-)Riemannian metric and is torsion-free.
The fundamental theorem o... |
https://en.wikipedia.org/wiki/Glossary%20of%20group%20theory | A group is a set together with an associative operation which admits an identity element and such that every element has an inverse.
Throughout the article, we use to denote the identity element of a group.
A
C
D
F
G
H
I
L
N
O
P
Q
R
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Basic definitions
Subgroup. A subset of a group which remains ... |
https://en.wikipedia.org/wiki/System%20of%20equations | In mathematics, a set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought. An equation system is usually classified in the same manner as single equations, namely as a:
System of linear equations,
System of nonlinear... |
https://en.wikipedia.org/wiki/Binary%20logarithm | In mathematics, the binary logarithm () is the power to which the number must be raised to obtain the value . That is, for any real number ,
For example, the binary logarithm of is , the binary logarithm of is , the binary logarithm of is , and the binary logarithm of is .
The binary logarithm is the logarithm t... |
https://en.wikipedia.org/wiki/Cos | Cos, COS, CoS, coS or Cos. may refer to:
Mathematics, science and technology
Carbonyl sulfide
Class of service (CoS or COS), a network header field defined by the IEEE 802.1p task group
Class of service (COS), a parameter in telephone systems
Cobalt sulfide
COS cells, cell lines COS-1 and COS-7
Cosine, a trigono... |
https://en.wikipedia.org/wiki/Geometry%20of%20numbers | Geometry of numbers is the part of number theory which uses geometry for the study of algebraic numbers. Typically, a ring of algebraic integers is viewed as a lattice in and the study of these lattices provides fundamental information on algebraic numbers. The geometry of numbers was initiated by .
The geometry of n... |
https://en.wikipedia.org/wiki/Skewes%27s%20number | In number theory, Skewes's number is any of several large numbers used by the South African mathematician Stanley Skewes as upper bounds for the smallest natural number for which
where is the prime-counting function and is the logarithmic integral function. Skewes's number is much larger, but it is now known that t... |
https://en.wikipedia.org/wiki/Effective%20results%20in%20number%20theory | For historical reasons and in order to have application to the solution of Diophantine equations, results in number theory have been scrutinised more than in other branches of mathematics to see if their content is effectively computable. Where it is asserted that some list of integers is finite, the question is whethe... |
https://en.wikipedia.org/wiki/Greeks%20%28finance%29 | In mathematical finance, the Greeks are the quantities (known in calculus as partial derivatives; first-order or higher) representing the sensitivity of the price of a derivative instrument such as an option to changes in one or more underlying parameters on which the value of an instrument or portfolio of financial in... |
https://en.wikipedia.org/wiki/Covering%20space | In topology, a covering or covering projection is a surjective map between topological spaces that, intuitively, locally acts like a projection of multiple copies of a space onto itself. In particular, coverings are special types of local homeomorphisms. If is a covering, is said to be a covering space or cover of , ... |
https://en.wikipedia.org/wiki/Ring%20theory | In algebra, ring theory is the study of rings—algebraic structures in which addition and multiplication are defined and have similar properties to those operations defined for the integers. Ring theory studies the structure of rings, their representations, or, in different language, modules, special classes of rings (g... |
https://en.wikipedia.org/wiki/William%20Kingdon%20Clifford | William Kingdon Clifford (4 May 18453 March 1879) was an English mathematician and philosopher. Building on the work of Hermann Grassmann, he introduced what is now termed geometric algebra, a special case of the Clifford algebra named in his honour. The operations of geometric algebra have the effect of mirroring, ro... |
https://en.wikipedia.org/wiki/Implicit%20function | In mathematics, an implicit equation is a relation of the form where is a function of several variables (often a polynomial). For example, the implicit equation of the unit circle is
An implicit function is a function that is defined by an implicit equation, that relates one of the variables, considered as the valu... |
https://en.wikipedia.org/wiki/Lemniscate%20of%20Bernoulli | In geometry, the lemniscate of Bernoulli is a plane curve defined from two given points and , known as foci, at distance from each other as the locus of points so that . The curve has a shape similar to the numeral 8 and to the ∞ symbol. Its name is from , which is Latin for "decorated with hanging ribbons". It is a... |
https://en.wikipedia.org/wiki/Existence%20theorem | In mathematics, an existence theorem is a theorem which asserts the existence of a certain object. It might be a statement which begins with the phrase "there exist(s)", or it might be a universal statement whose last quantifier is existential (e.g., "for all , , ... there exist(s) ..."). In the formal terms of symboli... |
https://en.wikipedia.org/wiki/Monodromy | In mathematics, monodromy is the study of how objects from mathematical analysis, algebraic topology, algebraic geometry and differential geometry behave as they "run round" a singularity. As the name implies, the fundamental meaning of monodromy comes from "running round singly". It is closely associated with coverin... |
https://en.wikipedia.org/wiki/Hypotenuse | In geometry, a hypotenuse is the longest side of a right-angled triangle, the side opposite the right angle. The length of the hypotenuse can be found using the Pythagorean theorem, which states that the square of the length of the hypotenuse equals the sum of the squares of the lengths of the other two sides. For exam... |
https://en.wikipedia.org/wiki/Glossary%20of%20ring%20theory | Ring theory is the branch of mathematics in which rings are studied: that is, structures supporting both an addition and a multiplication operation. This is a glossary of some terms of the subject.
For the items in commutative algebra (the theory of commutative rings), see Glossary of commutative algebra. For ring-the... |
https://en.wikipedia.org/wiki/Quadratic%20form | In mathematics, a quadratic form is a polynomial with terms all of degree two ("form" is another name for a homogeneous polynomial). For example,
is a quadratic form in the variables and . The coefficients usually belong to a fixed field , such as the real or complex numbers, and one speaks of a quadratic form over ... |
https://en.wikipedia.org/wiki/John%20Venn | John Venn, FRS, FSA (4 August 1834 – 4 April 1923) was an English mathematician, logician and philosopher noted for introducing Venn diagrams, which are used in logic, set theory, probability, statistics, and computer science. In 1866, Venn published The Logic of Chance, a groundbreaking book which espoused the frequen... |
https://en.wikipedia.org/wiki/Analytic%20number%20theory | In mathematics, analytic number theory is a branch of number theory that uses methods from mathematical analysis to solve problems about the integers. It is often said to have begun with Peter Gustav Lejeune Dirichlet's 1837 introduction of Dirichlet L-functions to give the first proof of Dirichlet's theorem on arithme... |
https://en.wikipedia.org/wiki/Deming%20regression | In statistics, Deming regression, named after W. Edwards Deming, is an errors-in-variables model which tries to find the line of best fit for a two-dimensional dataset. It differs from the simple linear regression in that it accounts for errors in observations on both the x- and the y- axis. It is a special case of tot... |
https://en.wikipedia.org/wiki/Diophantine%20approximation | In number theory, the study of Diophantine approximation deals with the approximation of real numbers by rational numbers. It is named after Diophantus of Alexandria.
The first problem was to know how well a real number can be approximated by rational numbers. For this problem, a rational number a/b is a "good" appro... |
https://en.wikipedia.org/wiki/Quartic%20equation | In mathematics, a quartic equation is one which can be expressed as a quartic function equaling zero. The general form of a quartic equation is
where a ≠ 0.
The quartic is the highest order polynomial equation that can be solved by radicals in the general case (i.e., one in which the coefficients can take any value).... |
https://en.wikipedia.org/wiki/Burnside%27s%20lemma | Burnside's lemma, sometimes also called Burnside's counting theorem, the Cauchy–Frobenius lemma, the orbit-counting theorem, or the lemma that is not Burnside's, is a result in group theory that is often useful in taking account of symmetry when counting mathematical objects. Its various eponyms are based on William Bu... |
https://en.wikipedia.org/wiki/Acute | Acute may refer to:
Language
Acute accent, a diacritic used in many modern written languages
Acute (phonetic), a perceptual classification
Science and mathematics
Acute angle
Acute triangle
Acute, a leaf shape in the glossary of leaf morphology
Acute (medicine), a disease that it is of short duration and of rec... |
https://en.wikipedia.org/wiki/Radical%20of%20an%20ideal | In ring theory, a branch of mathematics, the radical of an ideal of a commutative ring is another ideal defined by the property that an element is in the radical if and only if some power of is in . Taking the radical of an ideal is called radicalization. A radical ideal (or semiprime ideal) is an ideal that is equa... |
https://en.wikipedia.org/wiki/G%CE%B4%20set | {{DISPLAYTITLE:Gδ set}}
In the mathematical field of topology, a Gδ set is a subset of a topological space that is a countable intersection of open sets. The notation originated from the German nouns and .
Historically Gδ sets were also called inner limiting sets, but that terminology is not in use anymore.
Gδ sets,... |
https://en.wikipedia.org/wiki/Intersection%20%28disambiguation%29 | Intersection or intersect may refer to:
Intersection in mathematics, including:
Intersection (set theory), the set of elements common to some collection of sets
Intersection (geometry)
Intersection theory
Intersection (road), a place where two roads meet (line-line intersection)
Intersection (aviation), a virtua... |
https://en.wikipedia.org/wiki/Localization%20%28commutative%20algebra%29 | In commutative algebra and algebraic geometry, localization is a formal way to introduce the "denominators" to a given ring or module. That is, it introduces a new ring/module out of an existing ring/module R, so that it consists of fractions such that the denominator s belongs to a given subset S of R. If S is the se... |
https://en.wikipedia.org/wiki/Nilpotent | In mathematics, an element of a ring is called nilpotent if there exists some positive integer , called the index (or sometimes the degree), such that .
The term, along with its sister idempotent, was introduced by Benjamin Peirce in the context of his work on the classification of algebras.
Examples
This definit... |
https://en.wikipedia.org/wiki/Orbit%20%28dynamics%29 | In mathematics, specifically in the study of dynamical systems, an orbit is a collection of points related by the evolution function of the dynamical system. It can be understood as the subset of phase space covered by the trajectory of the dynamical system under a particular set of initial conditions, as the system ev... |
https://en.wikipedia.org/wiki/Sequent%20calculus | In mathematical logic, sequent calculus is a style of formal logical argumentation in which every line of a proof is a conditional tautology (called a sequent by Gerhard Gentzen) instead of an unconditional tautology. Each conditional tautology is inferred from other conditional tautologies on earlier lines in a formal... |
https://en.wikipedia.org/wiki/Absolute%20continuity | In calculus and real analysis, absolute continuity is a smoothness property of functions that is stronger than continuity and uniform continuity. The notion of absolute continuity allows one to obtain generalizations of the relationship between the two central operations of calculus—differentiation and integration. Thi... |
https://en.wikipedia.org/wiki/Simplicial%20complex | In mathematics, a simplicial complex is a set composed of points, line segments, triangles, and their n-dimensional counterparts (see illustration). Simplicial complexes should not be confused with the more abstract notion of a simplicial set appearing in modern simplicial homotopy theory. The purely combinatorial coun... |
https://en.wikipedia.org/wiki/Unit%20disk | In mathematics, the open unit disk (or disc) around P (where P is a given point in the plane), is the set of points whose distance from P is less than 1:
The closed unit disk around P is the set of points whose distance from P is less than or equal to one:
Unit disks are special cases of disks and unit balls; as such... |
https://en.wikipedia.org/wiki/Calculus%20%28dental%29 | In dentistry, calculus or tartar is a form of hardened dental plaque. It is caused by precipitation of minerals from saliva and gingival crevicular fluid (GCF) in plaque on the teeth. This process of precipitation kills the bacterial cells within dental plaque, but the rough and hardened surface that is formed provides... |
https://en.wikipedia.org/wiki/Method%20of%20Fluxions | Method of Fluxions () is a mathematical treatise by Sir Isaac Newton which served as the earliest written formulation of modern calculus. The book was completed in 1671 and published in 1736. Fluxion is Newton's term for a derivative. He originally developed the method at Woolsthorpe Manor during the closing of Cambrid... |
https://en.wikipedia.org/wiki/William%20Farr | William Farr CB (30 November 1807 – 14 April 1883) was a British epidemiologist, regarded as one of the founders of medical statistics.
Early life
William Farr was born in Kenley, Shropshire, to poor parents. He was effectively adopted by a local squire, Joseph Pryce, when Farr and his family moved to Dorrington. In ... |
https://en.wikipedia.org/wiki/Dimension%20of%20an%20algebraic%20variety | In mathematics and specifically in algebraic geometry, the dimension of an algebraic variety may be defined in various equivalent ways.
Some of these definitions are of geometric nature, while some other are purely algebraic and rely on commutative algebra. Some are restricted to algebraic varieties while others apply... |
https://en.wikipedia.org/wiki/Algebraic%20curve | In mathematics, an affine algebraic plane curve is the zero set of a polynomial in two variables. A projective algebraic plane curve is the zero set in a projective plane of a homogeneous polynomial in three variables. An affine algebraic plane curve can be completed in a projective algebraic plane curve by homogenizin... |
https://en.wikipedia.org/wiki/Almost | In set theory, when dealing with sets of infinite size, the term almost or nearly is used to refer to all but a negligible amount of elements in the set. The notion of "negligible" depends on the context, and may mean "of measure zero" (in a measure space), "finite" (when infinite sets are involved), or "countable" (wh... |
https://en.wikipedia.org/wiki/Well-defined%20expression | In mathematics, a well-defined expression or unambiguous expression is an expression whose definition assigns it a unique interpretation or value. Otherwise, the expression is said to be not well defined, ill defined or ambiguous. A function is well defined if it gives the same result when the representation of the inp... |
https://en.wikipedia.org/wiki/Implied%20volatility | In financial mathematics, the implied volatility (IV) of an option contract is that value of the volatility of the underlying instrument which, when input in an option pricing model (such as Black–Scholes), will return a theoretical value equal to the current market price of said option. A non-option financial instrum... |
https://en.wikipedia.org/wiki/Matrix%20decomposition | In the mathematical discipline of linear algebra, a matrix decomposition or matrix factorization is a factorization of a matrix into a product of matrices. There are many different matrix decompositions; each finds use among a particular class of problems.
Example
In numerical analysis, different decompositions are u... |
https://en.wikipedia.org/wiki/Proof%20of%20Bertrand%27s%20postulate | In mathematics, Bertrand's postulate (actually now a theorem) states that for each there is a prime such that . First conjectured in 1845 by Joseph Bertrand, it was first proven by Chebyshev, and a shorter but also advanced proof was given by Ramanujan.
The following elementary proof was published by Paul Erdős in 1... |
https://en.wikipedia.org/wiki/Mathematical%20fallacy | In mathematics, certain kinds of mistaken proof are often exhibited, and sometimes collected, as illustrations of a concept called mathematical fallacy. There is a distinction between a simple mistake and a mathematical fallacy in a proof, in that a mistake in a proof leads to an invalid proof while in the best-known e... |
https://en.wikipedia.org/wiki/Minimal%20polynomial | Minimal polynomial can mean:
Minimal polynomial (field theory)
Minimal polynomial of 2cos(2pi/n)
Minimal polynomial (linear algebra) |
https://en.wikipedia.org/wiki/Isometry | In mathematics, an isometry (or congruence, or congruent transformation) is a distance-preserving transformation between metric spaces, usually assumed to be bijective. The word isometry is derived from the Ancient Greek: ἴσος isos meaning "equal", and μέτρον metron meaning "measure".
Introduction
Given a metric spa... |
https://en.wikipedia.org/wiki/Tensor%20%28intrinsic%20definition%29 | In mathematics, the modern component-free approach to the theory of a tensor views a tensor as an abstract object, expressing some definite type of multilinear concept. Their properties can be derived from their definitions, as linear maps or more generally; and the rules for manipulations of tensors arise as an exten... |
https://en.wikipedia.org/wiki/Modus | Modus may refer to:
Modus, the Latin name for grammatical mood, in linguistics
Modus, the Latin name for mode (statistics)
Modus (company), an Alberta-based company
Modus (medieval music), a term used in several different technical meanings in medieval music theory
The Renault Modus, a small car
Modus (band), a ... |
https://en.wikipedia.org/wiki/Experimental%20mathematics | Experimental mathematics is an approach to mathematics in which computation is used to investigate mathematical objects and identify properties and patterns. It has been defined as "that branch of mathematics that concerns itself ultimately with the codification and transmission of insights within the mathematical comm... |
https://en.wikipedia.org/wiki/Mathematical%20problem | A mathematical problem is a problem that can be represented, analyzed, and possibly solved, with the methods of mathematics. This can be a real-world problem, such as computing the orbits of the planets in the solar system, or a problem of a more abstract nature, such as Hilbert's problems. It can also be a problem ref... |
https://en.wikipedia.org/wiki/Ordered%20exponential | The ordered exponential, also called the path-ordered exponential, is a mathematical operation defined in non-commutative algebras, equivalent to the exponential of the integral in the commutative algebras. In practice the ordered exponential is used in matrix and operator algebras.
Definition
Let be an algebra ov... |
https://en.wikipedia.org/wiki/Tensor%20field | In mathematics and physics, a tensor field assigns a tensor to each point of a mathematical space (typically a Euclidean space or manifold). Tensor fields are used in differential geometry, algebraic geometry, general relativity, in the analysis of stress and strain in materials, and in numerous applications in the ph... |
https://en.wikipedia.org/wiki/Thomas%20Heath%20%28classicist%29 | Sir Thomas Little Heath (; 5 October 1861 – 16 March 1940) was a British civil servant, mathematician, classical scholar, historian of ancient Greek mathematics, translator, and mountaineer. He was educated at Clifton College. Heath translated works of Euclid of Alexandria, Apollonius of Perga, Aristarchus of Samos, a... |
https://en.wikipedia.org/wiki/Knuth%27s%20up-arrow%20notation | In mathematics, Knuth's up-arrow notation is a method of notation for very large integers, introduced by Donald Knuth in 1976.
In his 1947 paper, R. L. Goodstein introduced the specific sequence of operations that are now called hyperoperations. Goodstein also suggested the Greek names tetration, pentation, etc., for ... |
https://en.wikipedia.org/wiki/Ergodic%20theory | Ergodic theory is a branch of mathematics that studies statistical properties of deterministic dynamical systems; it is the study of ergodicity. In this context, "statistical properties" refers to properties which are expressed through the behavior of time averages of various functions along trajectories of dynamical s... |
https://en.wikipedia.org/wiki/City%20Technology%20College | In England, a City Technology College (CTC) is an urban all-ability specialist school for students aged 11 to 18 specialising in science, technology and mathematics. They charge no fees and are independent of local authority control, being overseen directly by the Department for Education. One fifth of the capital cost... |
https://en.wikipedia.org/wiki/Theorema%20Egregium | Gauss's Theorema Egregium (Latin for "Remarkable Theorem") is a major result of differential geometry, proved by Carl Friedrich Gauss in 1827, that concerns the curvature of surfaces. The theorem says that Gaussian curvature can be determined entirely by measuring angles, distances and their rates on a surface, withou... |
https://en.wikipedia.org/wiki/Nicolas%20Chuquet | Nicolas Chuquet (; born ; died ) was a French mathematician. He invented his own notation for algebraic concepts and exponentiation. He may have been the first mathematician to recognize zero and negative numbers as exponents.
In 1475, Jehan Adam recorded the words "bymillion" and "trimillion" (for 1012 and 1018) and ... |
https://en.wikipedia.org/wiki/East%20Africa | East Africa, Eastern Africa, or East of Africa, is the eastern subregion of the African continent. In the United Nations Statistics Division scheme of geographic regions, 10-11-(16*) territories make up Eastern Africa:
Scientific consensus states the region of East Africa is where anatomically modern humans first evo... |
https://en.wikipedia.org/wiki/Initialized%20fractional%20calculus | In mathematical analysis, initialization of the differintegrals is a topic in fractional calculus.
Composition rule of differintegral
A certain counterintuitive property of the differintegral operator should be pointed out, namely the composition law. Although
wherein D−q is the left inverse of Dq, the converse is n... |
https://en.wikipedia.org/wiki/Minor%20%28linear%20algebra%29 | In linear algebra, a minor of a matrix A is the determinant of some smaller square matrix, cut down from A by removing one or more of its rows and columns. Minors obtained by removing just one row and one column from square matrices (first minors) are required for calculating matrix cofactors, which in turn are useful ... |
https://en.wikipedia.org/wiki/GAP%20%28computer%20algebra%20system%29 | GAP (Groups, Algorithms and Programming) is a computer algebra system for computational discrete algebra with particular emphasis on computational group theory.
History
GAP was developed at Lehrstuhl D für Mathematik (LDFM), Rheinisch-Westfälische Technische Hochschule Aachen, Germany from 1986 to 1997. After the reti... |
https://en.wikipedia.org/wiki/William%20Rankine | William John Macquorn Rankine (; 5 July 1820 – 24 December 1872) was a Scottish mechanical engineer who also contributed to civil engineering, physics and mathematics. He was a founding contributor, with Rudolf Clausius and William Thomson (Lord Kelvin), to the science of thermodynamics, particularly focusing on its F... |
https://en.wikipedia.org/wiki/Cycle%20space | In graph theory, a branch of mathematics, the (binary) cycle space of an undirected graph is the set of its even-degree subgraphs.
This set of subgraphs can be described algebraically as a vector space over the two-element finite field. The dimension of this space is the circuit rank of the graph. The same space can a... |
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